The best way to clip the nails if you are just starting is to shave it off bit by bit. This way your dog will let you know before you make the cut that will cut the quick. Depending on how badly you cut the quick, the bleeding may not stop on its own. You should have septic powder on hand to stop it if it happens. You will take a pinch of the powder and pack it into the end of the nail. the bleeding should stop within a minute. You can also get nitrate sticks to do the same thing.
You should use septic powder instead of corn starch even though it should also stop the bleeding because you want to protect it from infection. If you have just nicked the quick it will slowly produce a little bit of blood. If you have cut further into the blood vessel it will bleed much more and faster.
I teach all of my students to clip their dogs nails. If you are not familiar with the process I would have someone who is experienced show you first.
If you ever cut the quick, stay calm, stop the bleeding and then continue clipping the rest of the nails. If you freak out, so will they and they may the next time as well. You want to continue because you don't want their last memory to be of pain. If you cut the quick and don't continue it will be much harder to cut them next time.